What can be a complete mathematical knowledge?

Question

I started off with abstract algebra, and found in the next 3 pages that I needed a bit more of matrices, since I had no idea how functions could also be represented by matrices, so I dipped next into a book about matrices, but again the book says I'm expected to have a background knowledge of calculus, and I figure that same would be for calculus rotating me through a series of nought. Just as programming in a concrete sense is a series of electrical impulses guided by codes, I would like to put mathematics from the very concrete level and come to all these developed topics not rotating from here and there. It's not that high school maths didn't teach me even a bit on calculus but with more knowledge I believe it is true that we can solve complex calculus problems with general logic than the rules we step on to solve those problems regardless of the effort, that would be more understable thoroughly.

Editing my question, where is that--- I can start with learning that operations such as--- change in signs with positions in an equation are proved?

Answer 1

I'm not aware of one book or one summary that has everything there is to know about mathematics, since it's such a broad topic. My recommendation is to start from some first year undergraduate mathematics, like calculus and linear algebra, and continue from there. What mathematics do you know already

Answer 2

There is absolutely no such book, mathematics are way to broad. If you want to learn about a specific field in mathematics, there is top books in those categories. However, you will not find a book to learn about them all. It is simply not possible to feat mathematics in a single book. It would be like asking if there is a book about physic. You would have to say first if you want to learn about quantum physic, astronomy, relativity, mechanic...

Answer 3

From your question I interpret that you did not pay attention to maths in high school and want to catch up. So probably the first step would be to start from the beginning of high school material and do the work. After that you will have a better picture.